Non-conjugate boundary value problem of a third order differential equation

Abstract

This paper is devoted to prove the existence of the optimal interval where the Green’s function is negative definite. The left and right endpoints of the interval are found. Then, a new principle of comparison of a third-order differential equation is established. As an application of our results, the solvability of a non-conjugate boundary value problem is discussed.

Keywords

• third-order differential equation
• non-conjugate boundary condition
• green’s function
• principle of comparison
• upper and lower solutions